Question

If √3tan = 3sin , prove that sin2 – cos2 = 1/3. ​

Answer 1

Step-by-step explanation:

$\sqrt{3} \tan( \alpha ) = 3 \sin( \alpha )$

$\sqrt{3} \sin( \alpha ) \div \cos( \alpha ) = 3\sin( \alpha )$

now sin will

now sin will get cancelled both sides

$\sqrt{3} \div 3 = \cos( \alpha ) \\ \\ 1 \div \sqrt{3} = \cos( \alpha )$

$\cos( \alpha ) = b \div h$

find P by paethagorus

and put value

$p {}^{2} + b {}^{2} = h {}^{2} \\ \\ p = \sqrt{h {}^{2} - b { }^{2} } \\ \\ p = \sqrt{3 {?}^{2} - 1 {?}^{2} } \\ \\ p = \sqrt{2}$

now out value

$sin { \alpha }^{2} - \cos( { \alpha }^{2} ) \\ \\ \ \\ \sqrt{2 \div 3} {}^{2} - 1 \div \sqrt{3} { }^{2} \\ \\ 2 \div 3 - 1 \div 3 \\ \\ 1 \div 3$

hence proved I hope you like this

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